DABC be a tetrahedran such that AD is perpendicular to the base ABC and $∠ A B C = 30^{0}$ the volume of the tetrahedran is 18. If the value of $A B + B C + A D$ is minimum, then the length of AC is

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$6 \sqrt{2 - \sqrt{3}}$

$3 \sqrt{6 + 2 \sqrt{3}}$

$3 \sqrt{6 - 2 \sqrt{3}}$

$6 \sqrt{2 + \sqrt{3}}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$V = \frac{1}{3} B a s e A r e a . H e i g h t = 48 (\frac{1}{3} . \frac{1}{2} . A B . B C . \sin 30 \times A O) = 48 A O . A B . B C = 216 A M \geq G M \frac{A B + B C + A O}{3} = \sqrt[3]{216} = 6 A B + B C + A O = 18 A B = B C = A O = 6 A C^{2} = A B^{2} + B C^{2} - 2 A B . B C o s 30 6^{2} + 6^{2} - 2.6.6 \frac{\sqrt{3}}{2} A C = \sqrt{72 - 36 \sqrt{3}} = 6 \sqrt{2 - \sqrt{3}}$